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Probl. Peredachi Inf., 2006, Volume 42, Issue 1, Pages 34–42 (Mi ppi35)  

This article is cited in 10 scientific papers (total in 10 papers)

Coding Theory

Construction of Perfect $q$-ary Codes by Switchings of Simple Components

A. V. Los'

Novosibirsk State University

Abstract: We suggest a construction of perfect $q$-ary codes by sequential switchings of specialtype components (called simple components) of the Hamming code. We prove that such components are minimal. The construction yields a lower bound on the number of different $q$-ary codes; this is presently the best known bound. We show that this bound cannot be substantially improved using switchings of components of this type.

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English version:
Problems of Information Transmission, 2006, 42:1, 30–37

Bibliographic databases:

UDC: 621.391.15
Received: 23.06.2005
Revised: 12.09.2005

Citation: A. V. Los', “Construction of Perfect $q$-ary Codes by Switchings of Simple Components”, Probl. Peredachi Inf., 42:1 (2006), 34–42; Problems Inform. Transmission, 42:1 (2006), 30–37

Citation in format AMSBIB
\Bibitem{Los06}
\by A.~V.~Los'
\paper Construction of Perfect $q$-ary Codes by Switchings of Simple Components
\jour Probl. Peredachi Inf.
\yr 2006
\vol 42
\issue 1
\pages 34--42
\mathnet{http://mi.mathnet.ru/ppi35}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2214510}
\zmath{https://zbmath.org/?q=an:1096.94047}
\transl
\jour Problems Inform. Transmission
\yr 2006
\vol 42
\issue 1
\pages 30--37
\crossref{https://doi.org/10.1134/S0032946006010030}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645971024}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Romanov, “A survey of methods for constructing nonlinear perfect binary codes”, J. Appl. Industr. Math., 2:2 (2008), 252–269  mathnet  crossref  mathscinet  zmath
    2. F. I. Solov'eva, A. V. Los', “Intersections of $q$-ary perfect codes”, Siberian Math. J., 49:2 (2008), 375–382  mathnet  crossref  mathscinet  zmath  isi
    3. S. A. Malyugin, “On nonsystematic perfect codes over finite fields”, J. Appl. Industr. Math., 4:2 (2010), 218–230  mathnet  crossref  mathscinet  zmath
    4. F. I. Solov'eva, A. V. Los', “On partitions into perfect $q$-ary codes”, J. Appl. Industr. Math., 4:1 (2010), 136–142  mathnet  crossref  mathscinet  zmath
    5. E. V. Gorkunov, “Monomialnye avtomorfizmy lineinoi i prostoi komponent koda Khemminga”, Diskretn. analiz i issled. oper., 17:1 (2010), 11–33  mathnet  mathscinet  zmath
    6. A. V. Los, F. I. Soloveva, “O razbieniyakh prostranstva $F^N_q$ na affinno neekvivalentnye sovershennye $q$-znachnye kody”, Sib. elektron. matem. izv., 7 (2010), 425–434  mathnet
    7. A. V. Los, K. I. Burnakov, “O postroenii razbienii $(p+1)$-mernogo prostranstva vsekh $p$-znachnykh vektorov na kody Khemminga”, Sib. elektron. matem. izv., 8 (2011), 372–380  mathnet
    8. Heden O., Krotov D.S., “On the structure of non-full-rank perfect $q$-ary codes”, Adv. Math. Commun., 5:2 (2011), 149–156  crossref  mathscinet  zmath  isi  elib
    9. Potapov V.N., “On perfect 2-colorings of the $q$-ary $n$-cube”, Discrete Math., 312:6 (2012), 1269–1272  crossref  mathscinet  zmath  isi  elib
    10. Ostergard P.R.J., “Switching codes and designs”, Discrete Math., 312:3 (2012), 621–632  crossref  mathscinet  zmath  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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